Some Stylised Facts

1. College is expensive, both in actual costs and opportunity costs.
2. College graduates get a lot more money over their lifetime than non-graduates.
3. Just getting into a fancy college does not trigger this higher lifetime earning.
4. Completing some but not all of a degree does not trigger this higher lifetime earning.
5. The increase earning to college graduates tends to get larger as people get older.

Relative wage by educational attainment

Summary

Notes

‘Nordic’ here is Norway, Sweden, Finland, Denmark; ‘Europe’ is rest of Europe; ‘Pacific’ excludes USA.

Source: https://www.oecd-ilibrary.org/sites/9633d9f3-en/index.html?itemId=/content/component/9633d9f3-en#tablegrp-d1e7393-3a40fea345

US Specific

For most of these facts we can get very resilient data cross-nationally.

But there’s one group, which will be important in what follows, for which we really have to focus on US data.

That’s the ‘some college’ group.

Educational Attainment in the US (wiki)

https://www.bls.gov/emp/chart-unemployment-earnings-education.htm

US weekly pay by educational attainment. Actually a little over million dollar bonus for college grads

US Summary

Questions

1. Why do people go to college?
2. Why do employers pay so much extra for college graduates?

Ideally we should

• Consider radically different alternatives;
• Make everyone act rationally

Three Models

Well, three plus/minus one:

1. Human Capital
2. Selection
3. Signaling

And one extra (that may be one of the last two)

4. Honest signaling

Human Capital

College develops skills, and those skills are valuable.

Employers are rationally willing to pay for employees with those skills.

Students develop those skills because the (appropriately discounted) returns from developing them are larger than the costs of developing the skills.

Two Caveats

First, not everyone would develop skills by going to college, so not everyone should go.

For some people, going to college would be like building a fancy house next to a bunch of factories - not a good use of the land. (And that’s true even if the land might be very valuable, just not in the way that is enhanced by a fancy house.)

Two Caveats

Second, when we say college develops skills, we don’t mean that lectures develop skills. College also includes:

• Discussion sections;
• Feedback on work;
• Extra-curricular activities (theatre, sports, social organisations)
• Living with unfamiliar people

Which Skills

Should be a bit careful about the last couple of points.

• Not all US colleges are residential, or have extensive extra-curriculars.
• In many countries, living on campus is the exception not the norm, but the college wage premium is still high.

Problems

1. Causal mechanism
2. Gate-keeping (or lack of)
3. Sheepskin effect

Causal Mechanism

I can see (dimly) how the stuff we’re covering in 444 could be valuable for employers.

But the last big course I taught had a long unit on medieval epistemology, which I think is really philosophically valuable, but I have no idea how it leads to increased profits for an employer hiring someone who took the course.

And a commonly expressed worry is that lots of courses are like this.

Causal Mechanism

In reply, one might note that a lot of college courses set grads up with skills that come in useful in unexpected ways.

For instance, I’m told the people who are getting the best results out of image generating software are art history majors who have a better understanding of the ways in which pictures have been put together over the centuries.

In general, by not optimising for the present, we might produce good long term value.

Gatekeeping

If you go to a UM soccer match, where tickets are like $5, there is someone carefully checking the tickets.

On the human capital model, you’d think this lecture was much more valuable than a soccer match.

But there are no ticket collectors at the door. Anyone could walk in! We don’t act like it is some special value.

Gatekeeping

On the other hand, we don’t grade just anyone’s work, and we do restrict entry to the dorms.

If the lectures are a small part of the way in which we add skills, this might all make sense.

Sheepskin Effect

This is the name for the premium people get for finishing a college degree.

It is really substantial.

On the human capital model, you’d think that 3 years of college would get you 3/4 of the skill acquisition of 4 years of college.

But you really, really don’t see that in the wage data.

Sheepskin Effect

This is an objection to the human capital effect being all of the explanation for the college wage premium.

We’ll want to be careful as we proceed about distinguising:

• Reasons for thinking something isn’t a full explanation;
• Reasons for thinking something isn’t any part of the explanation.

Selection Effects

Not everyone gets admitted to fancy colleges. Here’s a model for the college wage premium.

• The premium is driven in large part by fancy schools; there isn’t much premium for non-selective schools.
• Not everyone can go to fancy schools; we literally don’t let everyone who applies in.
• The people we admit are independently valuable to employers.

Selection Effects

The strongest version of this theory is that this explains 100% of the college wage premium.

I think (for reasons I’ll soon get to) that is pretty implausible.

A weaker version is that it explains some of the college wage premium. And it would be surprising if it explained nothing.

Problems

1. Non-selective colleges.
2. Dropouts

Non-Selective

Some colleges admit most applicants; some colleges admit all applicants.

These colleges do (as far as I can tell) have a smaller wage premium than Michigan or similarly selective schools.

But they do still have a premium, and the selection model can’t explain this.

Dropouts

The strongest version of this theory is that it’s just the admission of getting into college that’s evidence you’ll get a high paying job.

If that were true, we’d expect to see a very different world to the one we actually see.

Dropouts

Why does admission to college mean you’ll get a high paying job?

1. Because it signals to employers (who are too stupid to see for themselves) that you’re smart. But then why bother actually going? Why wouldn’t an offer letter have the same market value as a degree?
2. Because it’s a sign to you that employers will, independently, be able to tell that you’re smart. But still why go to college? Perhaps because it’s so much fun. But there are more fun things that don’t involve calculus classes.

Toy Example

Spence gives an example where lots of variables are continuous.

We’re going to use a much simpler example, where the variables are binary.

This will obviously mean much less realism, but I think it doesn’t change the important strengths and weaknesses of the model. (As long as we don’t fuss about details.)

Though if you think I’m being too fair (or more likely too unfair) to the model for this reason, say so!

Structure

• Nature assigns each player a type, we’ll call it H for High Value, or L for Low Value.
• Worker goes to either C (for College), or B (for Beach). (In real world B might include starting work and using the money for more beach.)
• Employer decides whether to offer G (for Good) or P (for Poor) job.

Payouts

For Employer it’s easy

• They get 1 for offering Good to High, and Poor to Low; and 0 otherwise.

For Worker it’s a bit trickier

• Poor is worth 0, and Good is worth 4.
• Going to Beach costs 0.
• Going to College costs 5 if Low, and 1 if High.

Figure 1: College or Beach game

An Equilibria

This tree has a separating equilibrium:

• High workers go to College; Low workers go to Beach
• Employers offer Good jobs to College; Poor jobs to Beach

Details

The model is obviously silly in some ways.

• If the percentage of High goes above 50%, the natural equilibrium is that all workers go to Beach, and employers offer Good to everyone.
• But that problem goes away if you replace the binary variables with continuous ones.

Benefits of Model

Solves all the problems of previous models:

• Explains why finishing is rewarded; that shows you were willing to pay the (variable) price of going to college.
• Shows why it doesn’t matter what the content is, and why we don’t restrict attendance: it’s the degree that matters.

Downsides of Model

1. Inefficient
2. Wage premium for older workers
3. Costs are too high
4. Costs not correlated with skills

Inefficient

It’s really inefficient! The best workers in your workforce spending 4 years doing nothing useful just as a sorting device.

• Even if this makes sense for all individuals, someone at the systemic level should do something about it.
• Surprising that no country has solved this problem. (Though maybe the Nordics have.)

Age Profile

Why does the college wage premium rise with age?

• Model assumes employers can’t tell that Workers are High or Low.
• That’s plausible for 25-34.
• It’s not that plausible for 45-54. Why is it still an information set for those workers?

Costs of Model

The college wage premium is over one million dollars.

• You have to think calculus classes are really really painful to think that they are not worth a million dollars.

Cost Correlation

The model requires that college is more costly for Low workers than High workers.

• In my experience, the people who liked college most were the professional students who loved reading, getting into dorm room debates about esoteric details, etc.
• These were not the best employees!
• Even careful model requires tight correlation between felt cost of being at college and value to employer.

Honest Signals

There’s an annoying terminological point here. Different people use the phrase ‘honest signal’ in different ways. Some people use it for any situation where there is a separating equilibrium. I prefer using it for games like the following.

Revised Game

Low can’t go to college. At least, they can’t finish it.

Everything else in the graph is the same. So here’s the revised tree.

Figure 2: Honest College or Beach game

Biological Analogies

If we have time (we probably won’t) I’ll talk through how these models are used in biology.

The general idea is that sometimes it is worth doing something to signal, perfectly reliably, that you can do it.

Improvement?

This gets rid of the third problem - it’s not that Low refuses to take the million dollar bonus, it’s that they can’t.

I’m not sure it helps with the other three, but on the other hand, I thought that was the biggest problem with the first model.

Selection

This model has some features in common with the selection model.

What makes someone get a Good job is the same thing that causes them to (be able to) finish college: namely, that they are a High.

Your View

Which is most likely in your view to be most of the explanation of the college wage premium.

1. Human Capital
2. Selection
3. Signaling
4. Honest Signaling
5. None of the above/other

For Next Time

We’ll swing back to somewhat traditional epistemology, looking at how philosophers in the last decade or so have used some of the tools we’ve seen in this course to get a better understanding of